Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
716 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 249 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #26011969 | C2 | semidirect |
| 3. #26011464 | C2 | semidirect |
| 4. #519×C173 | C2 | semidirect |
| 7. C2×#14583827 | C4 | semidirect |
| 9. C2×Q8×D173 | C4 | semidirect |
| 63. C173 | #2884 | semidirect |
| 67. #519 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| #26011969 | 2 |
| #26011464 | 2 |
| #519×C173 | 2 |
| #2884 | 173 |